It is important in known methods that a first chilling (e.g. quenching)--after the annealing by which the starting state of an .alpha.-phase in an .alpha.+.beta. matrix is brought about suitably rapidly from the .beta.-phase--be carried out, so as to achieve a maximally uniform and fine crystalline grain structure in the form of martensitic .alpha.' grains and/or in the form of a fine lamellar .alpha.+.beta. phase, and to avoid thermal stresses which lead to cracks. Heretofore it has not been which lead to cracks. Heretofore it has not been possible to attain an optimal grain structure in crack-free parts, due to inappropriate chilling conditions in this important chilling step, particularly in the case of a large cross section.